3 Answers
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The original is lost, so we don't know. There were copies made in Latin and Old French which are available online... apparently, many copies were made upon its proclamation, in various languages, each intended for a particular audience.

Sorry! Books on Google Play is not available in your country yet Argh! Thanks though, I'll spoof my IP and check out the text later.
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YannisOct 16 '12 at 13:23

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The thing I like about this answer is it points to how muddled things were back then. Imagine thinking you could have legal documents imperfectly hand-copied and translated into multiple languages and consider them all authoritative.
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T.E.D.♦Oct 16 '12 at 13:32

It definitely wouldn't be English. In 1100, Old English was the language of the conquered Anglo-Saxon slaves (serfs). The Language of the conquerors of 1066 was Norman French or Anglo Norman. I'd put money on Latin.

Anglo-Norman was never the main administrative language of England: Latin was the major language of record in legal and other official documents for most of the medieval period. However, from the late 12th century until the early 15th century, Anglo-Norman French and Anglo-French were much used in law reports, charters, ordinances, official correspondence, and trade at all levels; they were the language of the King, his court and the upper class.

The original Charter of Liberties was probably written in Latin. I found an online source for the Latin text at archive.org. (The source is Select charters and other illustrations of English constitutional history (1913))

It looks like most of the English versions you see online are from a translation done in 1915 by Albert Beebe White and Wallce Notestein for their, Source Problems in English History (page 367).

Henry I was one of the early Norman kings. At the time Latin was considered the language of scholarship, French the language of the ruling classes, and English the language of the pesantry. Since the charter mainly deals with the rights of the nobility, English would seem to be a rather unlikely choice.

Continuing my research I found this Latin version of the charter. Not sure if we can conclusively say the original was written in Latin, but I think we have enough evidence that my bold claim that it was written in English is wrong. Thanks!
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YannisOct 16 '12 at 13:28